Effect of Rain Scavenging on Altitudinal istribution of Soluble aseous Pollutants in the Atosphere Tov Elperin a*, Andrew Foinykh a, Boris Krasovitov a, Alexander Vikhansky b a epartent of Mechanical Engineering, The Pearlstone Center for Aeronautical Engineering Studies, Ben-urion University of the Negev, P. O. B. 653, 8405, Israel b School of Engineering and Material Science, Queen Mary, University of London, Mile End Road, London E 4NS, UK Abstract We suggest a odel of rain scavenging of soluble gaseous pollutants in the atosphere. It is shown that below-cloud gas scavenging is deterined by non-stationary convective diffusion equation with the effective Peclet nuber. The obtained equation was analyzed nuerically in the case of log-noral droplet size distribution. Calculations of scavenging coefficient and the rates of precipitation scavenging are perfored for wet reoval of aonia (NH 3 ) and sulfur dioxide (SO ) fro the atosphere. It is shown that scavenging coefficient is non-stationary and height-dependent. It is found also that the scavenging coefficient strongly depends on initial concentration distribution of soluble gaseous pollutants in the atosphere. It is shown that in the case of linear distribution of the initial concentration of gaseous pollutants whereby the initial concentration of gaseous pollutants decreases with altitude, the scavenging coefficient increases with height in the beginning of rainfall. At the later stage of the rain scavenging coefficient decreases with height in the upper below-cloud layers of the atosphere.. Introduction Predicting cheical coposition of the atosphere and elucidating processes which affect atospheric cheistry is iportant for addressing probles related to air quality, cliate and ecosyste health. Wet deposition is very iportant in the reoval of gaseous pollutants fro the atosphere, and thus strongly affects global concentration of gaseous pollutants in the atosphere of Earth. Atospheric coposition is controlled by natural and anthropogenic eissions of gases, their subsequent transport and reoval processes. Wet deposition, including below-cloud scavenging by rains, is one of the ost iportant reoval echaniss that control * Corresponding author Tel.: +97 8 6477078 Fax: +97 8 64783 E-ail: elperin@bgu.ac.il the distribution, concentration and life-tie of any gaseous species in the atosphere. Rains, through the below-cloud scavenging and aqueous-phase processes, alter the cheical coposition of the atosphere on a global scale (see, e.g. Zhang et al. 006). Inorganic nitrogen in wet deposition is a significant source of nutrients for phytoplankton and has a direct ipact on the health of estuaries and coastal water bodies (see, e.g. Mizak et al. 005). Negative ipact of SO on visibility was indicated, e.g. by Watson (00), reen et al. (005) and by Tsai et al. (007).
Noenclature a c raindrop radius, total concentration of soluble trace gas in gas and liquid phases, ole ( ) c concentration of a soluble trace gas in a gaseous phase, ole ( ) c c concentration of a soluble gas at a lower Re = u d / ν external flow Reynolds nuber for a oving droplet Sc = ν / Schidt nuber Sh = β d / Sherwood nuber t tie, s T = tu / L diensionless tie boundary of a cloud, ole u velocity of a droplet, s ( ) c gr concentration of a soluble gas at a ground U wash-down front velocity, s level, ole ( ) ( ) ( ) C = c c c, 0 diensionless concentration of trace gas in an atosphere ( L) c concentration of dissolved gas in a d R L q c droplet, ole raindrop diaeter, coefficient of diffusion in a gaseous phase, s effective coefficient of diffusion, paraeter of solubility rainfall rate, s s distance between ground and lower boundary of a cloud, flux of dissolved gas, transferred by rain droplets, ole s Pe = UL/ Peclet nuber Mixed with water or reacting with other cheicals in the air SO has negative health effect. as scavenging by rain includes absorption of SO, NH 3 and other gases. Sulfur dioxide SO is eitted fro sokestacks as a result of various fossil fuels cobustion, e.g., crude oil and coal. The ain source of atospheric aonia is agriculture (see, e.g. Van z reek sybols β φ coordinate in a vertical direction, coefficient of ass transfer s volue fraction of droplets in the air µ dynaic viscosity of a fluid, kg s τ ch characteristic tie of concentration change in a gaseous phase, s, τ characteristic tie of diffusion process, s, Λ Subscripts 0 initial value c gr L scavenging coefficient, s value at a lower boundary of a cloud value at a ground gaseous phase liquid phase er Hoek, 998), and the reaining inor sources are industries, huans, pets, wild anials, landfills and households products. The contribution of vehicles to non-agricultural NH 3 eissions has been considered to be negligible until 995. In the last years, however, an increase of NH 3 eission due to introduction of petrol-engine vehicles equipped with
catalytic converters has been reported in the literature (see Fraser and Cass, 998). Concentration easureents of SO, NH 3 and other trace gases in the atospheric boundary layer revealed vertical (altitudinal) dependence of the concentrations (see eorgii 978; ravenhorst et al. 978; eorgii and Müller 974). Concentration of gases which are not associated with photosynthesis, e.g. SO and NH 3, has a axiu at the Earth surface and decreases with height over the continents. The concentration of NH 3 over the continents decreases rapidly with altitude, reaching a constant background concentration at the altitudes of about 500 above the ground in winter and at the altitudes of about 3000 above the ground on war days (see eorgii and Müller 974; eorgii 978). On war days the ground concentration of NH 3 is considerably higher than that on the cold days. Sulfur dioxide concentration in the ABL (atospheric boundary layer) is higher during winter than during suer because of the higher anthropogenic SO production. In contrast to the concentrations of SO and NH 3 over the continents, the profiles of concentration of these gases over the ocean have iniu at the ocean surface. This phenoenon is explained by a high solubility of SO and NH 3 in a sea water whereby the ocean acts as a sink of soluble gases (see eorgii and Müller 974; eorgii 978). Inforation about the evolution of the vertical profile of soluble gases with tie allows calculating fluxes of these gases in an the ABL. Vertical transport of soluble gases in the ABL is an integral part of the atospheric transport of gases and is iportant for understanding the global distribution pattern of soluble trace gases. An iproved understanding of the cycle of soluble gases is also essential for the analysis of global cliate change. Clouds and rains play essential role in vertical redistribution of SO, NH 3 and other soluble gases in the atosphere. Scavenging of soluble gases, e.g., SO, NH 3 by rains contributes to the evolution of vertical distribution of these gases. At the sae tie the existence of vertical gradients of the soluble gases in the atosphere affects the rate of gas absorption by rain droplets (see Elperin et al. 009). Note that the existing odels of global transport in the atosphere do not take into account the influence of rains on biogeocheical cycles of different gases. In spite of a large nuber of publications devoted to soluble gases scavenging by clouds (see, e.g., Elperin et al. 007 and Elperin et al. 008 and references therein) there are only a few studies on scavenging of these gases by rains. Hales (97, 00), Hales et al. (973) and Slinn (974) considered reoval of soluble pollutant gases fro gas plues. Hales (97, 00) and Hales et al. (973) assued that concentration of the dissolved gas in a droplet is equal to concentration of saturation in liquid, corresponding to concentration of a trace soluble gas in the atosphere at a certain height. Hales (97) showed that if a drop falls through a plue and eerges into a clean air before reaching the ground, it ay release ost of the soluble gaseous pollutants that has been reoved fro ore polluted regions. The significance of this effect is lowering the altitude of the regions with increased concentration of soluble gaseous pollutants under the influence of rain. Hales (00) considered a set of equations that correspond to five kinds of aussian plue forulation. This approach is valid for low gradients of concentration in a gaseous phase and for absorption of gases with low solubility, when τ << τ ch () where τ = a / β is a characteristic diffusion tie and τ = c u dc dz ch gr / is a characteristic 3
tie of concentration change in a gaseous phase. Slinn (974) showed that plue s washdown velocity can be calculated as w = I 0 H, where I 0 is a rainfall rate and H is a diensionless Henry s constant. The latter approach is valid for unifor droplet size distribution in the rain. Zhang et al. (006) investigated nuerically gas scavenging by drizzle developed fro low-level, war stratifor clouds using the approach of Ackeran et al (995), developed for odeling condensation nuclei and water droplets size distributions, and considered precipitation rates in the range fro 0.0 h up to 0.06 h. The conclusion of this study was that total droplet surface area is ore appropriate than the precipitation rate for paraeterizing scavenging coefficients, especially when precipitation has a large fraction of sall drops. ifferent aspects of soluble gaseous pollutants scavenging by rain droplets were discussed by Pruppacher and Klett (997), Wurzler (998), Stefan and Mircea (003), Slinn (977), Calderon et al. (008), Asan (995), Mircea et al. (000, 004), Kuar (985), Levine and Schwartz (98), ana et al. (975), Elperin and Foinykh (005). Asan (995) investigated absorption of highly soluble gases by rain using the approxiation of infinite solubility of absorbate in the absorbent and assuing that distribution of soluble gas in the atosphere during the rain is tie-dependent and unifor. The latter assuption allowed calculating nuerically the dependence of the scavenging coefficient on the rainfall rate in the atosphere. Power law dependence of the scavenging coefficient on the rainfall rate for aonia absorption by rain, which was predicted by Asan (995) theoretically, was confired experientally by Mizak et al. (005). All the above studies did not account for the dependence of scavenging coefficient on height, tie and initial profile of soluble gas in the atosphere. In this study we investigate the influence of the altitude absorbate inhoogenity in a gaseous phase on the rate of soluble gas scavenging by falling rain droplets. The proble is reduced to the equation of nonstationary convective diffusion with the effective Peclet nuber that depends on droplets size distribution (S). The obtained equation was solved nuerically for log-noral S with Feingold-Levin paraeterization (Feingold and Levin, 986), and tie and altitude dependence of the scavenging coefficient was analyzed.. escription of the odel In this study we consider absorption of a oderately soluble gas fro a ixture containing inert gas by falling rain droplets. At tie t = 0 rain droplets begin to fall and absorb gaseous pollutants (trace gases) fro the atosphere. It is assued that the initial concentration of the dissolved trace gas in rain droplets is equal to the concentration of saturation in liquid corresponding to concentration of a trace soluble gas in a cloud and that the initial distribution (at tie t = 0) of soluble trace gas in the atosphere is known. It ust be noted that for oderately soluble gases, only a sall fraction of the gas dissolves in the cloud water. Therefore the concentration of the oderately soluble gas in the interstitial air in a cloud is close to the concentration of the soluble gas in the below-cloud atosphere iediately adjacent to the cloud. Since the residence tie of droplets in the cloud is large, the equilibriu is established between the concentration of a oderately soluble gas in the interstitial air and concentration of the dissolved gas in the cloud droplets (see Asan 995). The goal of this study is to deterine an evolution of concentration distribution of soluble trace gases in the atosphere below the cloud under the influence of gas scavenging by falling rain droplets. Our analysis is not restricted to gases with 4
low solubility and is valid for all gases which obey Henri s law. The suggested odel is not constrained by a agnitude of a gradient of the soluble trace gas concentration in a gaseous phase. Following the approach suggested by Hales (97, 00) and Hales et al. (973), tie derivative of the ixed-average concentration of the dissolved gas in a falling droplet can be written as follows: dc dt L = τ ( ) ( L ) ( c c ), () where τ = ( a ) /(3β ) is a characteristic diffusion tie, is a solubility paraeter, β - ass transfer coefficient in a gaseous phase, ( L ) c - ixed-average concentration of the dissolved gas in a droplet, [ole l ], ( ) c - concentration of a soluble gaseous pollutant in a gaseous phase, [ole l ], a - raindrop radius. iensionless ass transfer coefficient for a falling droplet in a case of gaseous phase controlled ass transfer, Sh = β d /, can be written as follows (see, e.g. Seinfeld (006)): where Re () yields: 3 Sh = + 0.6 Re Sc, (3) c ν = u d /, Sc / = c L = ν. For sall τ Eq. d c τ. (4) dt Total concentration of soluble gaseous pollutant in gaseous and liquid phases reads: ( φ ) c ( ) + φc ( L) c = (5) As can be seen fro the Eq. (4) in the case when τ c d c dt << Eqs (4)-(5) yield: ( ) [ φ + φ] c = c, (6) where φ - volue fraction of droplets in the air. The total flux of the dissolved gas transferred by rain droplets is deterined by the following expression: q c where u - velocity of a droplet, L = φ u c, (7) ( L ) c - concentration of dissolved gas in a droplet. Using Eqs. (4) and (7) we obtain: q ( ) c = u c τ d c φ. (8) dt Equation of ass balance for soluble trace gas in the gaseous and liquid phases is as follows: c qc =. (9) t z Cobining Eqs. (4) (9) we obtain the following convective diffusion equation: where c t ( ) ( ) ( ) c c + U =, (0) z φu U =, ( φ) + φ z φτ u =, ( φ) + φ u = u U and u >> U. The ter in the right-hand side of Eq. (0) arises because we do not ake a siplifying assuption about equality between the instantaneous concentration of the dissolved gas in a droplet and concentration of saturation in liquid corresponding to the concentration of a trace soluble gas in an atosphere at a given height. In other words, Eq. (0) is valid when a characteristic diffusion tie and a characteristic tie of concentration change in a gaseous are of the sae order of agnitude. For exaple, for SO absorption by. diaeter water droplet, 4 U =. 0 s, 4.5 0 sec = τ =, 5.7 0 s, and for aonia absorption 5
by. diaeter water droplet U = 6.06 0 s, =.463 sec = τ, 5.97 0 s. In the present odel it was assued that the soluble gaseous species are olecularly dissolved in water droplets, and the olecules of these species do not dissociates into ions in the liquid phase (see Seinfeld and Pandis 006, Chapter 7). The initial and boundary conditions for Eq. (0) are as follows: t = 0, z = 0, z = L, c = f (z) () ( ) ( ) c c c, 0 =, () c, (3) z = 0 where L - distance between the ground and the lower boundary of a cloud. Equation of non-stationary convective diffusion (0) with initial and boundary conditions () - (3) (see, e.g. Leij and Toride 998) describes evolution of solvable trace gas distribution in the atosphere under the influence of rain. Equation (3) is a condition of ground ipereability for soluble gases. The volue fraction of a liquid phaseφ in Eq. (0) deterines the intensity of rain, R = uφ and U is the wash-down front velocity. Equation (0) iplies that trace gas in the atosphere is scavenged with a wash-down velocity U and is seared by diffusion. Equations (0) - (3) can be rewritten in the following for: C C C + = T Pe T = 0, η = 0, η =, η η (4) C = f (η), (5) C =, (6) ( ) C = 0, (7) η Where Pe = UL /, T = tu / L, C = c c c, 0. Assuing that the dependence of the terinal fall velocity of a liquid droplet depends on its diaeter is as follows (see Kessler, 969): u = c d, (8) where 30 [ c = s ], and u and d are expressed in SI units, we obtain the following forula for Peclet nuber: 3 4 U L 6 L c d Pe = = + 0.6 5 6 3 c d ν For aonia, NH 3 (9) 4 = 0. 0 = 55, 6 ν = 5 0 NH, air 3 s, s. Consequently, for aonia scavenging by diaeter water droplets falling in the air and for L = 000, Pe = 7. In a case of sulfur dioxide, SO 4 = 0. 0 Pe = 5.53 0 s, 30 and SO = 3. If the initial distribution of a trace gas in the atosphere is linear, the boundary condition given by Eq. (5) becoes T = 0, ( ) η ( ) ( ) ( ) + c gr,0 c c, 0 C =. (0) 3. Results and discussions The above odel of atospheric trace gases scavenging by liquid precipitation was applied to study the evolution of trace soluble gas concentration in the atosphere caused by rain. Results of nuerical solution of Eqs. (4) (7) with linear initial distribution of soluble trace gas in the atosphere for and. ( ) ( ) gr, 0 c c,0 = c are presented at Figs. 6
approxiately 600 of precipitation can wash out k of atosphere fro the aonia gas. At the sae tie for wet reoval of sulfur dioxide fro the atosphere of the sae altitude the considerably higher aount of precipitation is required. Fig.. Evolution of aonia distribution in the atosphere caused by rain scavenging Calculations are perfored for scavenging of NH 3 and SO by rain. Wet reoval of soluble gases fro the atosphere strongly depends on the raindrops diaeter that is deterined by droplet size distribution (S). In our calculations we assued the log-noral size distribution of raindrops with Feingold and Levin paraeterization (Feingold and Levin, 986) based on the long-tie easureents of rain drops size spectra in Israel: ( ln d ln ) ln N = d d n d exp r, π d lnσ σ ( ) () 0. 0.3 N d = 7 R ; d r = 0.7 R ( ) ; 4 σ =.43 3 0 R, where R is the rain intensity ( h ). Voluetric fraction of raindrops in the atosphere was assued to be equal to 6 0. Inspection of Figs. and shows that the larger is the solubility of the trace gas in water, the saller it is the quantity of precipitation required to washout it. For instance, inspection of Fig. reveals that Fig.. Evolution of sulfur dioxide distribution in the atosphere caused by rain scavenging In the calculations the initial concentration of dissolved trace gas in rain drops is assued equal to the concentration of saturation in a liquid corresponding to the concentration of a trace soluble gas in a cloud. Therefore the soluble gas in the belowcloud atosphere can be washed down only up to the concentration of soluble gas in the interstitial air in a cloud. Note that for gaseous pollutants their concentration at the ground is always larger than the concentration in a cloud (see e.g., eorgii and Müller, 974; eorgii, 978; ravenhorst et al., 978). Inspection of Figs. shows that the thickness of the layer washed down by precipitation strongly depends on the rainfall aount and also depends on the gas solubility. Using the obtained nuerical solution of the equation (4) with the boundary conditions (5) (7) we also calculated the scavenging coefficient for soluble trace gas absorption fro the atosphere: 7
c Λ =. () ( ) c t The dependence of the scavenging coefficient vs. altitude in the case of aonia wash out is shown in Figs. 3 4. Inspection of Figs. 3 4 shows that scavenging coefficient strongly depends on the initial distribution of soluble trace gas concentration in the atosphere. Fig. 3. ependence of scavenging coefficient vs. altitude for aonia wash out (linear initial distribution of aonia in the atosphere c gr, 0 c c,0 = 00.0 ). The previous studies have showed that the scavenging coefficient which is easured or calculated under the assuption of the unifor soluble trace gas distribution ay not accurately predict wet deposition of soluble trace gases in the presence of a gradient of concentration of trace gases in the atosphere (see e.g. Assan, 995; Mizak et al., 005; Calderon et al., 008). The suggested odel takes into account the initial concentration gradient of soluble species in the atosphere. Calculations were perfored for linear initial distribution of aonia in the atosphere and different ratios of the aonia concentration in a ( ) ( ) cloud and at the ground: c gr, 0 c c,0 = 00.0 (see Fig. ( ) ( ) 3) and c gr, 0 c c,0 =.0 (see Fig. 4). Fig. 4. ependence of scavenging coefficient vs. altitude for aonia wash out (linear initial distribution of ( ) ( ) aonia in the atosphere c gr, 0 c c,0 =.0 ) As can be seen fro these plots the scavenging coefficient increases with the increase of the soluble species concentration gradient. The analysis of the plots on Figs. 3 4 shows that the high values of the scavenging coefficient Λ in the below-cloud atosphere iediately adjacent to the cloud at the early stage of a rain is explained by high rates of gas absorption by falling rain droplets. High rates of ass transfer between the rain droplets and soluble gas are caused by thin concentration boundary layers in droplets and in a gaseous phase at the initial stage of gas-liquid contact. For linear profile of soluble gas in the atosphere, at the early stage of a rain, the scavenging coefficient increases with height. In the case when τ << τ ch the ass flux to the rain droplets falling in an atosphere with a non-unifor initial concentration profile of soluble gas is constant. Therefore the rate of change of concentration in a gaseous phase c / t is constant. At the sae tie 8
the distribution of the concentration in an atosphere ( ) c decreases with height. Consequently Λ increases with height at the early stage of rain whereby the initial concentration profile of the soluble gas in the atosphere is not disturbed significantly. Scavenging of soluble gas begins in the upper atosphere and the front of scavenging propagates downwards with the wash down velocity that is proportional to Henry s constant and rain intensity (see Eq. 0). Concentration of a soluble gas in the below-cloud layer decreases to the concentration of a soluble gas in the interstitial air in a cloud. The subsequent rain droplets fall in the below-cloud atosphere without absorbing soluble gas. This explains the decrease of the scavenging coefficient in the upper below-cloud layers of the atosphere at the later stages of rain whereby the initial concentration profile of the soluble gas in the atosphere changes significantly. Note that the soluble gas in the below-cloud layer is washed out only to the concentration of the soluble gas in the interstitial air in a cloud. At the ground the value of the scavenging coefficient increases with tie because the concentration at the ground decreases faster than the rate of concentration change. ependences of scavenging coefficient on the rate of precipitation are shown in Figs. 5 and 6. The dependences of the scavenging coefficient on rain intensity are plotted for the early stage of rain (Fig. 5) as well as for the advanced stage of rain (Fig. 6). As can be seen fro these plots the scavenging coefficient increases with rain intensity increase. In spite of the nuerous theoretical calculations and easureents of scavenging coefficient available in the literature (see e.g., Beilke, 970; Sperber and Haeed, 986; Shishock and e Pena, 989; Renard et al., 004; Mizak et al., 005) the Fig. 5. ependence of scavenging coefficient vs. rain intensity for aonia wash out at the early stage of rain 4 (diensionless tie T = 5 0 ; linear initial distribution ( ) ( ) of aonia in the atosphere c gr, 0 c c,0 = 50.0 ). coparison of the predicted values of scavenging coefficient with those calculated fro the easured concentrations of aonia in rainwater reveals large discrepancies. Fig. 6. ependence of scavenging coefficient vs. rain intensity for aonia wash out at the later stage of rain (diensionless tie T = 0. 05 ; linear initial distribution of ( ) ( ) aonia in the atosphere c gr, 0 c c,0 = 50.0 ). 9
In particular, for wet deposition of aonia very different values of scavenging coefficient are reported in the literature, in the range fro less that 0 5 (s ) (Sperber and Haeed, 986) to larger than 0 3 (s ) (in Mizak et al., 005) are reported. This large scatter of data is entioned in several studies and reviews (see e.g., Renard et al., 004). The wide range of variation of the agnitude of scavenging coefficient is caused by dependence of scavenging coefficient on the altitude, tie, initial gradient of the soluble gas concentration in the below-cloud atosphere, droplet size distribution as well as on eteorological conditions (wind, teperature etc.) and difficulties associated with evaluating scavenging coefficient fro the experients. Conclusions In this study we developed a odel for scavenging of soluble trace gases in the atosphere by rain. It is shown that gas scavenging is deterined by nonstationary convective diffusion equation with the effective Peclet nuber that depends on droplet size distribution (S). The obtained equation was analyzed nuerically in the case of log-noral S with Feingold-Levin paraeterization (Feingold and Levin, 986). The siple for of the obtained equation allows analyzing the dependence of the rate of soluble gas scavenging on different paraeters, e.g. rain intensity, gas solubility, gradient of absorbate concentration in a gaseous phase etc. Using the developed odel we calculated scavenging coefficient and the rates of scavenging of different trace gases (SO and NH 3 ). The obtained results can be suarized as follows:. It is deonstrated that scavenging coefficient for the wash out of soluble atospheric gases by rain is tie-dependent. It is shown that value of scavenging coefficient at the ground increases with tie whereas the value of scavenging coefficient in the below-cloud atosphere iediately adjacent to the cloud decreases with the aount of precipitation.. It is shown that scavenging coefficient in the atosphere is height-dependent. Scavenging of soluble gas begins in the upper atosphere and scavenging front propagates downwards with wash down velocity and is seared by diffusion. We have found that in the case of linear initial distribution of concentration of gaseous pollutants whereby the initial concentration of gaseous pollutants decreases with altitude, the scavenging coefficient Λ c increases with height at an early stage of rain. At the advanced stage of rain scavenging coefficient decreases with height in the upper below-cloud layers of the atosphere. 3. It is found that scavenging coefficient strongly depends on the initial distribution of soluble trace gas concentration in the atosphere. Calculations perfored for linear distribution of the soluble gaseous species in the atosphere show that the scavenging coefficient increases with the increase of soluble species gradient. The developed odel can be used for the analysis of precipitation scavenging of hazardous gases in the atosphere by rain and for validating advanced odels for predicting scavenging of soluble gases by rain. REFERENCES Ackeran, A. S., Toon, O.B., Hobbs, P.V., 995. A odel for particle icrophysics, turbulent ixing, and radiative transfer in the stratocuulus-topped arine boundary-layer and coparison with easureents. 0
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